Modes in SAW grating resonators

Abstract

A Rayleigh wave of finite width, propagating along the surface of an isotropic medium, is shown to obey approximately a paraxial wave equation if the width is large compared with a wavelength. Results of laser wave propagation can be applied to the Rayleigh-wave case. Furthermore, an equation is derived for the two-dimensional Rayleigh-wave propagation underneath a grating surface. A grating of finite width is shown to provide transverse confinement (guidance) of the wave. The mode patterns are obtained of the fundamental and higher-order guided modes under uniform gratings of finite width. For a grating resonator formed of two uniform gratings separated by a quarter-wave section, a variational expression is developed for the resonance frequencies. Using a simple mode pattern for the trial solution, the resonance frequencies of the higher-order modes are evaluated. They all lie on the high side of the Bragg frequency, increasing with increasing mode number.